A boy plays with a ball, and he drops it from a height of 1.5 m. Every time the ball hits the ground, it…
A boy plays with a ball, and he drops it from a height of 1.5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing?
4
5
6
7
Solution
Initial height = 150 cm. Heights after successive hits: 1st hit $\to (4/5)\times150 = 120$, 2nd $\to 96$, 3rd $\to 76.8$, 4th $\to 61.44$, 5th $\to 49.15$. After the 5th hit the rebound height (49.15 cm) is below 50 cm, so the ball does not bounce after the 6th hit. The ball hits the ground 6 times.